The synthetic aperture radar (SAR) imaging methods based on compressive sensing endure great computational complexity since they have to deal with a large measurement matrix when processing the raw data. An efficient ℓq regularisation algorithm for SAR imaging is proposed, which uses a decoupling operator constructed by means of chirp scaling. It can reduce the computational complexity from the square order to the linear logarithm order compared with the conventional ℓq regularisation‐based imaging algorithm while preserving the equivalent imaging quality. The proposed algorithm is efficient in the sense that it allows reconstruction of the sparse scenes with the sub‐sampling data.
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